LMFDB - Embedded newform 2717.1.db.c.2001.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2717,1,Mod(142,2717)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2717, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 8]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2717.142");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2717 = 11 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2717.db (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.35595963932$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{45}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{45} - \cdots)$

Embedding invariants

Embedding label			2001.3
Root			$0.961262 - 0.275637i$ of defining polynomial
Character	$\chi$	$=$	2717.2001
Dual form			2717.1.db.c.2144.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10209 - 0.924765i) q^{2} +(-0.823868 - 0.299864i) q^{3} +(0.185769 - 1.05355i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(0.990268 - 1.71519i) q^{7} +(-0.0502092 - 0.0869649i) q^{8} +(-0.177204 - 0.148692i) q^{9} +O(q^{10})$	\(q+(1.10209 - 0.924765i) q^{2} +(-0.823868 - 0.299864i) q^{3} +(0.185769 - 1.05355i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(0.990268 - 1.71519i) q^{7} +(-0.0502092 - 0.0869649i) q^{8} +(-0.177204 - 0.148692i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.468969 + 0.812278i) q^{12} +(0.939693 - 0.342020i) q^{13} +(-0.494786 - 2.80607i) q^{14} +(0.869525 + 0.316481i) q^{16} -0.332800 q^{18} +(-0.559193 + 0.829038i) q^{19} +(-1.33017 + 1.11615i) q^{21} +(1.35192 + 0.492057i) q^{22} +(0.294524 - 1.67033i) q^{23} +(0.0152882 + 0.0867035i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(0.719340 - 1.24593i) q^{26} +(0.539776 + 0.934920i) q^{27} +(-1.62308 - 1.36192i) q^{28} +(1.34533 - 0.489660i) q^{32} +(-0.152245 - 0.863423i) q^{33} +(-0.189572 + 0.159070i) q^{36} +(0.150383 + 1.43080i) q^{38} -0.876742 q^{39} +(-0.704030 - 0.256246i) q^{41} +(-0.433799 + 2.46020i) q^{42} +(1.00528 - 0.365893i) q^{44} +(-1.22007 - 2.11322i) q^{46} +(-0.621473 - 0.521478i) q^{48} +(-1.46126 - 2.53098i) q^{49} +(-0.719340 + 1.24593i) q^{50} +(-0.185769 - 1.05355i) q^{52} +(-0.346450 + 1.96482i) q^{53} +(1.45947 + 0.531202i) q^{54} -0.198882 q^{56} +(0.709299 - 0.515336i) q^{57} +(-0.430514 + 0.156694i) q^{63} +(0.567193 - 0.982407i) q^{64} +(-0.966251 - 0.810781i) q^{66} +(-0.743520 + 1.28781i) q^{69} +(-0.00403369 + 0.0228762i) q^{72} +(-1.52045 - 0.553400i) q^{73} +0.876742 q^{75} +(0.769549 + 0.743145i) q^{76} +1.98054 q^{77} +(-0.966251 + 0.810781i) q^{78} +(-0.124187 - 0.704302i) q^{81} +(-1.01287 + 0.368656i) q^{82} +(-0.882948 + 1.52931i) q^{83} +(0.928810 + 1.60875i) q^{84} +(0.0502092 - 0.0869649i) q^{88} +(0.343916 - 1.95045i) q^{91} +(-1.70506 - 0.620589i) q^{92} -1.25521 q^{96} +(-3.95101 - 1.43805i) q^{98} +(0.0401688 - 0.227809i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} - 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * q^78 + 6 * q^81 + 3 * q^82 - 12 * q^84 - 3 * q^88 - 6 * q^91 - 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

$n$	$210$	$287$	$2224$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.104528	−	0.994522i	$-0.466667\pi$
$2$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.997564	+	0.0697565i	$0.0222222\pi$
$3$	−0.823868	−	0.299864i	−0.823868	−	0.299864i	−0.104528	−	0.994522i	$-0.533333\pi$
$3$	−0.823868	−	0.299864i	−0.823868	−	0.299864i	−0.719340	+	0.694658i	$0.755556\pi$
$4$	0.185769	−	1.05355i	0.185769	−	1.05355i
$5$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$5$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$6$	−1.18528	+	0.431408i	−1.18528	+	0.431408i
$7$	0.990268	−	1.71519i	0.990268	−	1.71519i	0.374607	−	0.927184i	$-0.377778\pi$
$7$	0.990268	−	1.71519i	0.990268	−	1.71519i	0.615661	−	0.788011i	$-0.288889\pi$
$8$	−0.0502092	−	0.0869649i	−0.0502092	−	0.0869649i
$9$	−0.177204	−	0.148692i	−0.177204	−	0.148692i
$10$		0			0
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$12$	−0.468969	+	0.812278i	−0.468969	+	0.812278i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$14$	−0.494786	−	2.80607i	−0.494786	−	2.80607i
$15$		0			0
$16$	0.869525	+	0.316481i	0.869525	+	0.316481i
$17$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$17$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$18$	−0.332800			−0.332800
$19$	−0.559193	+	0.829038i	−0.559193	+	0.829038i
$19$	−0.559193	+	0.829038i	−0.559193	+	0.829038i
$20$		0			0
$21$	−1.33017	+	1.11615i	−1.33017	+	1.11615i
$22$	1.35192	+	0.492057i	1.35192	+	0.492057i
$23$	0.294524	−	1.67033i	0.294524	−	1.67033i	−0.374607	−	0.927184i	$-0.622222\pi$
$23$	0.294524	−	1.67033i	0.294524	−	1.67033i	0.669131	−	0.743145i	$-0.266667\pi$
$24$	0.0152882	+	0.0867035i	0.0152882	+	0.0867035i
$25$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$26$	0.719340	−	1.24593i	0.719340	−	1.24593i
$27$	0.539776	+	0.934920i	0.539776	+	0.934920i
$28$	−1.62308	−	1.36192i	−1.62308	−	1.36192i
$29$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$29$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	1.34533	−	0.489660i	1.34533	−	0.489660i
$33$	−0.152245	−	0.863423i	−0.152245	−	0.863423i
$34$		0			0
$35$		0			0
$36$	−0.189572	+	0.159070i	−0.189572	+	0.159070i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.150383	+	1.43080i	0.150383	+	1.43080i
$39$	−0.876742			−0.876742
$40$		0			0
$41$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.0348995	−	0.999391i	$-0.511111\pi$
$41$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.669131	+	0.743145i	$0.733333\pi$
$42$	−0.433799	+	2.46020i	−0.433799	+	2.46020i
$43$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$43$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$44$	1.00528	−	0.365893i	1.00528	−	0.365893i
$45$		0			0
$46$	−1.22007	−	2.11322i	−1.22007	−	2.11322i
$47$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$47$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$48$	−0.621473	−	0.521478i	−0.621473	−	0.521478i
$49$	−1.46126	−	2.53098i	−1.46126	−	2.53098i
$50$	−0.719340	+	1.24593i	−0.719340	+	1.24593i
$51$		0			0
$52$	−0.185769	−	1.05355i	−0.185769	−	1.05355i
$53$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.104528	+	0.994522i	$0.533333\pi$
$53$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.241922	+	0.970296i	$0.577778\pi$
$54$	1.45947	+	0.531202i	1.45947	+	0.531202i
$55$		0			0
$56$	−0.198882			−0.198882
$57$	0.709299	−	0.515336i	0.709299	−	0.515336i
$58$		0			0
$59$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$59$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$60$		0			0
$61$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$61$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$62$		0			0
$63$	−0.430514	+	0.156694i	−0.430514	+	0.156694i
$64$	0.567193	−	0.982407i	0.567193	−	0.982407i
$65$		0			0
$66$	−0.966251	−	0.810781i	−0.966251	−	0.810781i
$67$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$67$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$68$		0			0
$69$	−0.743520	+	1.28781i	−0.743520	+	1.28781i
$70$		0			0
$71$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$71$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$72$	−0.00403369	+	0.0228762i	−0.00403369	+	0.0228762i
$73$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.559193	−	0.829038i	$-0.688889\pi$
$73$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.961262	+	0.275637i	$0.911111\pi$
$74$		0			0
$75$	0.876742			0.876742
$76$	0.769549	+	0.743145i	0.769549	+	0.743145i
$77$	1.98054			1.98054
$78$	−0.966251	+	0.810781i	−0.966251	+	0.810781i
$79$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$79$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$80$		0			0
$81$	−0.124187	−	0.704302i	−0.124187	−	0.704302i
$82$	−1.01287	+	0.368656i	−1.01287	+	0.368656i
$83$	−0.882948	+	1.52931i	−0.882948	+	1.52931i	−0.0348995	+	0.999391i	$0.511111\pi$
$83$	−0.882948	+	1.52931i	−0.882948	+	1.52931i	−0.848048	+	0.529919i	$0.822222\pi$
$84$	0.928810	+	1.60875i	0.928810	+	1.60875i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.0502092	−	0.0869649i	0.0502092	−	0.0869649i
$89$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$89$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$90$		0			0
$91$	0.343916	−	1.95045i	0.343916	−	1.95045i
$92$	−1.70506	−	0.620589i	−1.70506	−	0.620589i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.25521			−1.25521
$97$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$97$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$98$	−3.95101	−	1.43805i	−3.95101	−	1.43805i
$99$	0.0401688	−	0.227809i	0.0401688	−	0.227809i
$100$	0.185769	+	1.05355i	0.185769	+	1.05355i
$101$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$101$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$102$		0			0
$103$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	0.848048	−	0.529919i	$-0.177778\pi$
$103$	−0.0348995	−	0.0604477i	−0.0348995	−	0.0604477i	−0.882948	+	0.469472i	$0.844444\pi$
$104$	−0.0769249	−	0.0645477i	−0.0769249	−	0.0645477i
$105$		0			0
$106$	1.43518	+	2.48580i	1.43518	+	2.48580i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	1.08526	−	0.395001i	1.08526	−	0.395001i
$109$	−0.317271	−	1.79933i	−0.317271	−	1.79933i	−0.559193	−	0.829038i	$-0.688889\pi$
$109$	−0.317271	−	1.79933i	−0.317271	−	1.79933i	0.241922	−	0.970296i	$-0.422222\pi$
$110$		0			0
$111$		0			0
$112$	1.40389	−	1.17800i	1.40389	−	1.17800i
$113$	1.92252			1.92252			0.961262	−	0.275637i	$-0.0888889\pi$
$113$	1.92252			1.92252			0.961262	+	0.275637i	$0.0888889\pi$
$114$	0.305148	−	1.22388i	0.305148	−	1.22388i
$115$		0			0
$116$		0			0
$117$	−0.217372	−	0.0791171i	−0.217372	−	0.0791171i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	0.503189	+	0.422226i	0.503189	+	0.422226i
$124$		0			0
$125$		0			0
$126$	−0.329561	+	0.570816i	−0.329561	+	0.570816i
$127$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$127$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$128$	−0.0347900	−	0.197304i	−0.0347900	−	0.197304i
$129$		0			0
$130$		0			0
$131$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$131$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$132$	−0.937938			−0.937938
$133$	0.868210	+	1.78009i	0.868210	+	1.78009i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$137$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$138$	0.371498	+	2.10687i	0.371498	+	2.10687i
$139$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$139$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.766044	+	0.642788i	0.766044	+	0.642788i
$144$	−0.107025	−	0.185373i	−0.107025	−	0.185373i
$145$		0			0
$146$	−2.18745	+	0.796166i	−2.18745	+	0.796166i
$147$	0.444939	+	2.52337i	0.444939	+	2.52337i
$148$		0			0
$149$	−1.83832	−	0.669092i	−1.83832	−	0.669092i	−0.990268	−	0.139173i	$-0.955556\pi$
$149$	−1.83832	−	0.669092i	−1.83832	−	0.669092i	−0.848048	−	0.529919i	$-0.822222\pi$
$150$	0.966251	−	0.810781i	0.966251	−	0.810781i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	0.100174	+	0.00700483i	0.100174	+	0.00700483i
$153$		0			0
$154$	2.18273	−	1.83153i	2.18273	−	1.83153i
$155$		0			0
$156$	−0.162871	+	0.923689i	−0.162871	+	0.923689i
$157$	0.232387	+	1.31793i	0.232387	+	1.31793i	0.848048	+	0.529919i	$0.177778\pi$
$157$	0.232387	+	1.31793i	0.232387	+	1.31793i	−0.615661	+	0.788011i	$0.711111\pi$
$158$		0			0
$159$	0.874607	−	1.51486i	0.874607	−	1.51486i
$160$		0			0
$161$	−2.57328	−	2.15924i	−2.57328	−	2.15924i
$162$	−0.788180	−	0.661361i	−0.788180	−	0.661361i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−0.400754	+	0.694126i	−0.400754	+	0.694126i
$165$		0			0
$166$	0.441163	+	2.50196i	0.441163	+	2.50196i
$167$	−0.333843	+	1.89332i	−0.333843	+	1.89332i	0.104528	+	0.994522i	$0.466667\pi$
$167$	−0.333843	+	1.89332i	−0.333843	+	1.89332i	−0.438371	+	0.898794i	$0.644444\pi$
$168$	0.163853	+	0.0596375i	0.163853	+	0.0596375i
$169$	0.766044	−	0.642788i	0.766044	−	0.642788i
$170$		0			0
$171$	0.222362	−	0.0637612i	0.222362	−	0.0637612i
$172$		0			0
$173$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$173$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$174$		0			0
$175$	−0.343916	+	1.95045i	−0.343916	+	1.95045i
$176$	0.160682	+	0.911271i	0.160682	+	0.911271i
$177$		0			0
$178$		0			0
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$180$		0			0
$181$	−0.370646	−	0.311009i	−0.370646	−	0.311009i	0.438371	−	0.898794i	$-0.355556\pi$
$181$	−0.370646	−	0.311009i	−0.370646	−	0.311009i	−0.809017	+	0.587785i	$0.800000\pi$
$182$	−1.42468	−	2.46762i	−1.42468	−	2.46762i
$183$		0			0
$184$	−0.160048	+	0.0582526i	−0.160048	+	0.0582526i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.13809			2.13809
$190$		0			0
$191$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$191$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$192$	−0.761880	+	0.639294i	−0.761880	+	0.639294i
$193$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.978148	−	0.207912i	$-0.0666667\pi$
$193$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.615661	+	0.788011i	$0.288889\pi$
$194$		0			0
$195$		0			0
$196$	−2.93796	+	1.06933i	−2.93796	+	1.06933i
$197$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	−0.961262	−	0.275637i	$-0.911111\pi$
$197$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	0.719340	+	0.694658i	$0.244444\pi$
$198$	−0.166400	−	0.288213i	−0.166400	−	0.288213i
$199$	0.856733	+	0.718885i	0.856733	+	0.718885i	0.961262	−	0.275637i	$-0.0888889\pi$
$199$	0.856733	+	0.718885i	0.856733	+	0.718885i	−0.104528	+	0.994522i	$0.533333\pi$
$200$	0.0769249	+	0.0645477i	0.0769249	+	0.0645477i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.0943624	−	0.0343451i	−0.0943624	−	0.0343451i
$207$	−0.300554	+	0.252195i	−0.300554	+	0.252195i
$208$	0.925329			0.925329
$209$	−0.997564	−	0.0697565i	−0.997564	−	0.0697565i
$210$		0			0
$211$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$211$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$212$	2.00567	+	0.730003i	2.00567	+	0.730003i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	0.0542035	−	0.0938832i	0.0542035	−	0.0938832i
$217$		0			0
$218$	−2.01362	−	1.68963i	−2.01362	−	1.68963i
$219$	1.08671	+	0.911858i	1.08671	+	0.911858i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$223$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$224$	0.492375	−	2.79240i	0.492375	−	2.79240i
$225$	0.217372	+	0.0791171i	0.217372	+	0.0791171i
$226$	2.11880	−	1.77788i	2.11880	−	1.77788i
$227$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$227$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$228$	−0.411165	−	0.843013i	−0.411165	−	0.843013i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	−1.63170	−	0.593891i	−1.63170	−	0.593891i
$232$		0			0
$233$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$233$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$234$	−0.312729	+	0.113824i	−0.312729	+	0.113824i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.559193	+	0.968551i	0.559193	+	0.968551i	0.997564	+	0.0697565i	$0.0222222\pi$
$239$	0.559193	+	0.968551i	0.559193	+	0.968551i	−0.438371	+	0.898794i	$0.644444\pi$
$240$		0			0
$241$	−1.65940	+	0.603972i	−1.65940	+	0.603972i	−0.990268	−	0.139173i	$-0.955556\pi$
$241$	−1.65940	+	0.603972i	−1.65940	+	0.603972i	−0.669131	+	0.743145i	$0.733333\pi$
$242$	0.249824	+	1.41682i	0.249824	+	1.41682i
$243$	0.0785820	−	0.445661i	0.0785820	−	0.445661i
$244$		0			0
$245$		0			0
$246$	0.945021			0.945021
$247$	−0.241922	+	0.970296i	−0.241922	+	0.970296i
$248$		0			0
$249$	1.18602	−	0.995186i	1.18602	−	0.995186i
$250$		0			0
$251$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$251$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$252$	0.0851087	+	0.482675i	0.0851087	+	0.482675i
$253$	1.59381	−	0.580099i	1.59381	−	0.580099i
$254$		0			0
$255$		0			0
$256$	0.648189	+	0.543895i	0.648189	+	0.543895i
$257$	0.473442	+	0.397265i	0.473442	+	0.397265i	0.848048	−	0.529919i	$-0.177778\pi$
$257$	0.473442	+	0.397265i	0.473442	+	0.397265i	−0.374607	+	0.927184i	$0.622222\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$263$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$264$	−0.0674434	+	0.0565917i	−0.0674434	+	0.0565917i
$265$		0			0
$266$	2.60302	+	1.15894i	2.60302	+	1.15894i
$267$		0			0
$268$		0			0
$269$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.669131	−	0.743145i	$-0.266667\pi$
$269$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.0348995	+	0.999391i	$0.488889\pi$
$270$		0			0
$271$	0.0840186	+	0.476493i	0.0840186	+	0.476493i	0.997564	+	0.0697565i	$0.0222222\pi$
$271$	0.0840186	+	0.476493i	0.0840186	+	0.476493i	−0.913545	+	0.406737i	$0.866667\pi$
$272$		0			0
$273$	−0.868210	+	1.50378i	−0.868210	+	1.50378i
$274$		0			0
$275$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$276$	1.21865	+	1.02257i	1.21865	+	1.02257i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0840186	−	0.476493i	0.0840186	−	0.476493i	−0.913545	−	0.406737i	$-0.866667\pi$
$281$	0.0840186	−	0.476493i	0.0840186	−	0.476493i	0.997564	−	0.0697565i	$-0.0222222\pi$
$282$		0			0
$283$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$283$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$284$		0			0
$285$		0			0
$286$	1.43868			1.43868
$287$	−1.13669	+	0.953796i	−1.13669	+	0.953796i
$288$	−0.311206	−	0.113270i	−0.311206	−	0.113270i
$289$	0.173648	−	0.984808i	0.173648	−	0.984808i
$290$		0			0
$291$		0			0
$292$	−0.865486	+	1.49906i	−0.865486	+	1.49906i
$293$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$293$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$294$	2.82389	+	2.36953i	2.82389	+	2.36953i
$295$		0			0
$296$		0			0
$297$	−0.539776	+	0.934920i	−0.539776	+	0.934920i
$298$	−2.64475	+	0.962610i	−2.64475	+	0.962610i
$299$	−0.294524	−	1.67033i	−0.294524	−	1.67033i
$300$	0.162871	−	0.923689i	0.162871	−	0.923689i
$301$		0			0
$302$	1.10209	−	0.924765i	1.10209	−	0.924765i
$303$		0			0
$304$	−0.748607	+	0.543895i	−0.748607	+	0.543895i
$305$		0			0
$306$		0			0
$307$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$307$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$308$	0.367922	−	2.08659i	0.367922	−	2.08659i
$309$	0.0106265	+	0.0602660i	0.0106265	+	0.0602660i
$310$		0			0
$311$	−0.438371	+	0.759281i	−0.438371	+	0.759281i	−0.997564	−	0.0697565i	$-0.977778\pi$
$311$	−0.438371	+	0.759281i	−0.438371	+	0.759281i	0.559193	+	0.829038i	$0.311111\pi$
$312$	0.0440205	+	0.0762458i	0.0440205	+	0.0762458i
$313$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.882948	−	0.469472i	$-0.844444\pi$
$313$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.615661	−	0.788011i	$-0.711111\pi$
$314$	1.47489	+	1.23758i	1.47489	+	1.23758i
$315$		0			0
$316$		0			0
$317$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$317$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$318$	−0.436996	−	2.47833i	−0.436996	−	2.47833i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−4.83278			−4.83278
$323$		0			0
$324$	−0.765085			−0.765085
$325$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$326$		0			0
$327$	−0.278165	+	1.57755i	−0.278165	+	1.57755i
$328$	0.0130644	+	0.0740918i	0.0130644	+	0.0740918i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	1.44718	+	1.21432i	1.44718	+	1.21432i
$333$		0			0
$334$	1.38295	+	2.39534i	1.38295	+	2.39534i
$335$		0			0
$336$	−1.50986	+	0.549544i	−1.50986	+	0.549544i
$337$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$337$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$338$	0.249824	−	1.41682i	0.249824	−	1.41682i
$339$	−1.58391	−	0.576495i	−1.58391	−	0.576495i
$340$		0			0
$341$		0			0
$342$	0.186099	−	0.275903i	0.186099	−	0.275903i
$343$	−3.80763			−3.80763
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$347$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$348$		0			0
$349$	0.0348995	−	0.0604477i	0.0348995	−	0.0604477i	−0.848048	−	0.529919i	$-0.822222\pi$
$349$	0.0348995	−	0.0604477i	0.0348995	−	0.0604477i	0.882948	+	0.469472i	$0.155556\pi$
$350$	1.42468	+	2.46762i	1.42468	+	2.46762i
$351$	0.826986	+	0.693923i	0.826986	+	0.693923i
$352$	1.09672	+	0.920260i	1.09672	+	0.920260i
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	2.54077	+	0.924765i	2.54077	+	0.924765i
$359$	−1.29929	+	1.09023i	−1.29929	+	1.09023i	−0.309017	+	0.951057i	$0.600000\pi$
$359$	−1.29929	+	1.09023i	−1.29929	+	1.09023i	−0.990268	+	0.139173i	$0.955556\pi$
$360$		0			0
$361$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$362$	−0.696096			−0.696096
$363$	0.671624	−	0.563559i	0.671624	−	0.563559i
$364$	−1.99100	−	0.724664i	−1.99100	−	0.724664i
$365$		0			0
$366$		0			0
$367$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.559193	−	0.829038i	$-0.311111\pi$
$367$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.961262	+	0.275637i	$0.0888889\pi$
$368$	0.784724	−	1.35918i	0.784724	−	1.35918i
$369$	0.0866551	+	0.150091i	0.0866551	+	0.150091i
$370$		0			0
$371$	3.02697	+	2.53993i	3.02697	+	2.53993i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	2.35638	−	1.97723i	2.35638	−	1.97723i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	2.01362	−	1.68963i	2.01362	−	1.68963i
$383$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$383$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$384$	−0.0305019	+	0.172985i	−0.0305019	+	0.172985i
$385$		0			0
$386$	2.29298	−	0.834577i	2.29298	−	0.834577i
$387$		0			0
$388$		0			0
$389$	−0.160147	−	0.134379i	−0.160147	−	0.134379i	0.559193	−	0.829038i	$-0.311111\pi$
$389$	−0.160147	−	0.134379i	−0.160147	−	0.134379i	−0.719340	+	0.694658i	$0.755556\pi$
$390$		0			0
$391$		0			0
$392$	−0.146738	+	0.254157i	−0.146738	+	0.254157i
$393$		0			0
$394$	0.120876	+	0.685521i	0.120876	+	0.685521i
$395$		0			0
$396$	−0.232545	−	0.0846394i	−0.232545	−	0.0846394i
$397$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$397$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$398$	1.60900			1.60900
$399$	−0.181505	−	1.72691i	−0.181505	−	1.72691i
$400$	−0.925329			−0.925329
$401$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$401$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$409$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−0.0701677	+	0.0255389i	−0.0701677	+	0.0255389i
$413$		0			0
$414$	−0.0980175	+	0.555885i	−0.0980175	+	0.555885i
$415$		0			0
$416$	1.09672	−	0.920260i	1.09672	−	0.920260i
$417$		0			0
$418$	−1.16392	+	0.845635i	−1.16392	+	0.845635i
$419$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$419$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$420$		0			0
$421$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$421$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$422$		0			0
$423$		0			0
$424$	0.188265	−	0.0685229i	0.188265	−	0.0685229i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.438371	−	0.759281i	−0.438371	−	0.759281i
$430$		0			0
$431$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	−0.309017	−	0.951057i	$-0.600000\pi$
$431$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	0.374607	+	0.927184i	$0.377778\pi$
$432$	0.173464	+	0.983766i	0.173464	+	0.983766i
$433$	0.194206	−	1.10140i	0.194206	−	1.10140i	−0.719340	−	0.694658i	$-0.755556\pi$
$433$	0.194206	−	1.10140i	0.194206	−	1.10140i	0.913545	−	0.406737i	$-0.133333\pi$
$434$		0			0
$435$		0			0
$436$	−1.95462			−1.95462
$437$	1.22007	+	1.17821i	1.22007	+	1.17821i
$438$	2.04091			2.04091
$439$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$439$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$440$		0			0
$441$	−0.117394	+	0.665776i	−0.117394	+	0.665776i
$442$		0			0
$443$	1.65940	−	0.603972i	1.65940	−	0.603972i	0.669131	−	0.743145i	$-0.266667\pi$
$443$	1.65940	−	0.603972i	1.65940	−	0.603972i	0.990268	+	0.139173i	$0.0444444\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.31389	+	1.10249i	1.31389	+	1.10249i
$448$	−1.12335	−	1.94569i	−1.12335	−	1.94569i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	0.312729	−	0.113824i	0.312729	−	0.113824i
$451$	−0.130100	−	0.737831i	−0.130100	−	0.737831i
$452$	0.357145	−	2.02547i	0.357145	−	2.02547i
$453$	−0.823868	−	0.299864i	−0.823868	−	0.299864i
$454$	1.78322	−	1.49630i	1.78322	−	1.49630i
$455$		0			0
$456$	−0.0804295	−	0.0358095i	−0.0804295	−	0.0358095i
$457$	−1.11839			−1.11839			−0.559193	−	0.829038i	$-0.688889\pi$
$457$	−1.11839			−1.11839			−0.559193	+	0.829038i	$0.688889\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.0363024	+	0.205881i	0.0363024	+	0.205881i	0.997564	−	0.0697565i	$-0.0222222\pi$
$461$	0.0363024	+	0.205881i	0.0363024	+	0.205881i	−0.961262	+	0.275637i	$0.911111\pi$
$462$	−2.34749	+	0.854418i	−2.34749	+	0.854418i
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$467$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$468$	−0.123735	+	0.214314i	−0.123735	+	0.214314i
$469$		0			0
$470$		0			0
$471$	0.203743	−	1.15548i	0.203743	−	1.15548i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.241922	−	0.970296i	0.241922	−	0.970296i
$476$		0			0
$477$	0.353544	−	0.296659i	0.353544	−	0.296659i
$478$	1.51196	+	0.550310i	1.51196	+	0.550310i
$479$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$479$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	−1.27028	+	2.20019i	−1.27028	+	2.20019i
$483$	1.47257	+	2.55056i	1.47257	+	2.55056i
$484$	0.819514	+	0.687654i	0.819514	+	0.687654i
$485$		0			0
$486$	−0.325527	−	0.563830i	−0.325527	−	0.563830i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$491$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$492$	0.538311	−	0.451697i	0.538311	−	0.451697i
$493$		0			0
$494$	0.630676	+	1.29308i	0.630676	+	1.29308i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.386786	−	2.19357i	0.386786	−	2.19357i
$499$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$499$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$500$		0			0
$501$	0.842779	−	1.45974i	0.842779	−	1.45974i
$502$	−0.444576	−	0.770029i	−0.444576	−	0.770029i
$503$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$503$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$504$	0.0352427	+	0.0295721i	0.0352427	+	0.0295721i
$505$		0			0
$506$	1.22007	−	2.11322i	1.22007	−	2.11322i
$507$	−0.823868	+	0.299864i	−0.823868	+	0.299864i
$508$		0			0
$509$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$509$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$510$		0			0
$511$	−2.45485	+	2.05986i	−2.45485	+	2.05986i
$512$	1.41769			1.41769
$513$	−1.07692	−	0.0753058i	−1.07692	−	0.0753058i
$514$	0.889153			0.889153
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$521$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$522$		0			0
$523$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$523$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$524$		0			0
$525$	0.868210	−	1.50378i	0.868210	−	1.50378i
$526$		0			0
$527$		0			0
$528$	0.140876	−	0.798950i	0.140876	−	0.798950i
$529$	−1.76356	−	0.641884i	−1.76356	−	0.641884i
$530$		0			0
$531$		0			0
$532$	2.03670	−	0.584014i	2.03670	−	0.584014i
$533$	−0.749213			−0.749213
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.286126	−	1.62270i	−0.286126	−	1.62270i
$538$	1.01287	−	0.368656i	1.01287	−	0.368656i
$539$	1.46126	−	2.53098i	1.46126	−	2.53098i
$540$		0			0
$541$	0.943248	+	0.791479i	0.943248	+	0.791479i	0.978148	−	0.207912i	$-0.0666667\pi$
$541$	0.943248	+	0.791479i	0.943248	+	0.791479i	−0.0348995	+	0.999391i	$0.511111\pi$
$542$	0.533241	+	0.447442i	0.533241	+	0.447442i
$543$	0.212103	+	0.367373i	0.212103	+	0.367373i
$544$		0			0
$545$		0			0
$546$	0.433799	+	2.46020i	0.433799	+	2.46020i
$547$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$547$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$548$		0			0
$549$		0			0
$550$	−1.43868			−1.43868
$551$		0			0
$552$	0.149326			0.149326
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.669131	−	0.743145i	$-0.733333\pi$
$557$	−0.704030	+	0.256246i	−0.704030	+	0.256246i	−0.0348995	+	0.999391i	$0.511111\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.348048	−	0.602837i	−0.348048	−	0.602837i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.33099	−	0.484442i	−1.33099	−	0.484442i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$	0.819514	−	0.687654i	0.819514	−	0.687654i
$573$	−1.50528	−	0.547878i	−1.50528	−	0.547878i
$574$	−0.370700	+	2.10234i	−0.370700	+	2.10234i
$575$	0.294524	+	1.67033i	0.294524	+	1.67033i
$576$	−0.246584	+	0.0897493i	−0.246584	+	0.0897493i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	−0.719340	−	1.24593i	−0.719340	−	1.24593i
$579$	−1.13914	−	0.955850i	−1.13914	−	0.955850i
$580$		0			0
$581$	1.74871	+	3.02885i	1.74871	+	3.02885i
$582$		0			0
$583$	−1.87481	+	0.682374i	−1.87481	+	0.682374i
$584$	0.0282144	+	0.160012i	0.0282144	+	0.160012i
$585$		0			0
$586$	0.469516	+	0.170890i	0.469516	+	0.170890i
$587$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$587$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$588$	2.74115			2.74115
$589$		0			0
$590$		0			0
$591$	0.324961	−	0.272675i	0.324961	−	0.272675i
$592$		0			0
$593$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	0.615661	+	0.788011i	$0.288889\pi$
$593$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	−0.848048	+	0.529919i	$0.822222\pi$
$594$	0.269698	+	1.52954i	0.269698	+	1.52954i
$595$		0			0
$596$	−1.04642	+	1.81245i	−1.04642	+	1.81245i
$597$	−0.490268	−	0.849169i	−0.490268	−	0.849169i
$598$	−1.86925	−	1.56849i	−1.86925	−	1.56849i
$599$	−1.10209	−	0.924765i	−1.10209	−	0.924765i	−0.104528	−	0.994522i	$-0.533333\pi$
$599$	−1.10209	−	0.924765i	−1.10209	−	0.924765i	−0.997564	+	0.0697565i	$0.977778\pi$
$600$	−0.0440205	−	0.0762458i	−0.0440205	−	0.0762458i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	0.185769	−	1.05355i	0.185769	−	1.05355i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.346352	+	1.38914i	−0.346352	+	1.38914i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.333843	−	1.89332i	−0.333843	−	1.89332i	−0.438371	−	0.898794i	$-0.644444\pi$
$613$	−0.333843	−	1.89332i	−0.333843	−	1.89332i	0.104528	−	0.994522i	$-0.466667\pi$
$614$	−2.54077	+	0.924765i	−2.54077	+	0.924765i
$615$		0			0
$616$	−0.0994411	−	0.172237i	−0.0994411	−	0.172237i
$617$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$617$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$618$	0.0674434	+	0.0565917i	0.0674434	+	0.0565917i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	1.72060	−	0.626248i	1.72060	−	0.626248i
$622$	0.219031	+	1.24219i	0.219031	+	1.24219i
$623$		0			0
$624$	−0.762349	−	0.277472i	−0.762349	−	0.277472i
$625$	0.766044	−	0.642788i	0.766044	−	0.642788i
$626$	−2.81448			−2.81448
$627$	0.800944	+	0.356603i	0.800944	+	0.356603i
$628$	1.43167			1.43167
$629$		0			0
$630$		0			0
$631$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$631$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−1.43350	−	1.20285i	−1.43350	−	1.20285i
$637$	−2.23878	−	1.87856i	−2.23878	−	1.87856i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.0121205	+	0.0687386i	0.0121205	+	0.0687386i	0.990268	−	0.139173i	$-0.0444444\pi$
$641$	0.0121205	+	0.0687386i	0.0121205	+	0.0687386i	−0.978148	+	0.207912i	$0.933333\pi$
$642$		0			0
$643$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$643$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$644$	−2.75289	+	2.30995i	−2.75289	+	2.30995i
$645$		0			0
$646$		0			0
$647$	−0.483844			−0.483844			−0.241922	−	0.970296i	$-0.577778\pi$
$647$	−0.483844			−0.483844			−0.241922	+	0.970296i	$0.577778\pi$
$648$	−0.0550142	+	0.0461624i	−0.0550142	+	0.0461624i
$649$		0			0
$650$	−0.249824	+	1.41682i	−0.249824	+	1.41682i
$651$		0			0
$652$		0			0
$653$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$653$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$654$	1.15230	+	1.99585i	1.15230	+	1.99585i
$655$		0			0
$656$	−0.531075	−	0.445625i	−0.531075	−	0.445625i
$657$	0.187144	+	0.324143i	0.187144	+	0.324143i
$658$		0			0
$659$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$659$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$660$		0			0
$661$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$661$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$662$		0			0
$663$		0			0
$664$	0.177328			0.177328
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.93268	+	0.703437i	1.93268	+	0.703437i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−1.24299	+	2.15292i	−1.24299	+	2.15292i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−0.826986	−	0.693923i	−0.826986	−	0.693923i
$676$	−0.534899	−	0.926473i	−0.534899	−	0.926473i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−2.27873	+	0.829391i	−2.27873	+	0.829391i
$679$		0			0
$680$		0			0
$681$	−1.33305	−	0.485189i	−1.33305	−	0.485189i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−0.0258676	−	0.246113i	−0.0258676	−	0.246113i
$685$		0			0
$686$	−4.19636	+	3.52116i	−4.19636	+	3.52116i
$687$		0			0
$688$		0			0
$689$	0.346450	+	1.96482i	0.346450	+	1.96482i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−0.350958	−	0.294489i	−0.350958	−	0.294489i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.0174375	−	0.0988928i	−0.0174375	−	0.0988928i
$699$		0			0
$700$	1.99100	+	0.724664i	1.99100	+	0.724664i
$701$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$701$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$702$	1.55313			1.55313
$703$		0			0
$704$	1.13439			1.13439
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$709$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.88931	−	0.687654i	1.88931	−	0.687654i
$717$	−0.170268	−	0.965640i	−0.170268	−	0.965640i
$718$	−0.423726	+	2.40307i	−0.423726	+	2.40307i
$719$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$719$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$	−0.138239			−0.138239
$722$	−1.27028	−	0.675419i	−1.27028	−	0.675419i
$723$	1.54823			1.54823
$724$	−0.396517	+	0.332717i	−0.396517	+	0.332717i
$725$		0			0
$726$	0.219031	−	1.24219i	0.219031	−	1.24219i
$727$	0.343916	+	1.95045i	0.343916	+	1.95045i	0.309017	+	0.951057i	$0.400000\pi$
$727$	0.343916	+	1.95045i	0.343916	+	1.95045i	0.0348995	+	0.999391i	$0.488889\pi$
$728$	−0.186888	+	0.0680217i	−0.186888	+	0.0680217i
$729$	−0.555962	+	0.962955i	−0.555962	+	0.962955i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.882948	−	1.52931i	−0.882948	−	1.52931i	−0.848048	−	0.529919i	$-0.822222\pi$
$733$	−0.882948	−	1.52931i	−0.882948	−	1.52931i	−0.0348995	−	0.999391i	$-0.511111\pi$
$734$	1.16392	−	2.01596i	1.16392	−	2.01596i
$735$		0			0
$736$	−0.421661	−	2.39136i	−0.421661	−	2.39136i
$737$		0			0
$738$	0.234301	+	0.0852786i	0.234301	+	0.0852786i
$739$	0.573931	−	0.481585i	0.573931	−	0.481585i	−0.309017	−	0.951057i	$-0.600000\pi$
$739$	0.573931	−	0.481585i	0.573931	−	0.481585i	0.882948	+	0.469472i	$0.155556\pi$
$740$		0			0
$741$	0.490268	−	0.726852i	0.490268	−	0.726852i
$742$	5.68483			5.68483
$743$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$743$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.383857	−	0.139713i	0.383857	−	0.139713i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.160147	−	0.134379i	−0.160147	−	0.134379i	0.559193	−	0.829038i	$-0.311111\pi$
$751$	−0.160147	−	0.134379i	−0.160147	−	0.134379i	−0.719340	+	0.694658i	$0.755556\pi$
$752$		0			0
$753$	−0.270928	+	0.469262i	−0.270928	+	0.469262i
$754$		0			0
$755$		0			0
$756$	0.397191	−	2.25258i	0.397191	−	2.25258i
$757$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$757$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$758$		0			0
$759$	−1.48704			−1.48704
$760$		0			0
$761$	1.23132			1.23132			0.615661	−	0.788011i	$-0.288889\pi$
$761$	1.23132			1.23132			0.615661	+	0.788011i	$0.288889\pi$
$762$		0			0
$763$	−3.40039	−	1.23764i	−3.40039	−	1.23764i
$764$	0.339416	−	1.92492i	0.339416	−	1.92492i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.370928	−	0.642466i	−0.370928	−	0.642466i
$769$	0.573931	+	0.481585i	0.573931	+	0.481585i	0.882948	−	0.469472i	$-0.155556\pi$
$769$	0.573931	+	0.481585i	0.573931	+	0.481585i	−0.309017	+	0.951057i	$0.600000\pi$
$770$		0			0
$771$	−0.270928	−	0.469262i	−0.270928	−	0.469262i
$772$	0.907241	−	1.57139i	0.907241	−	1.57139i
$773$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$773$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.300766			−0.300766
$779$	0.606126	−	0.440376i	0.606126	−	0.440376i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.469596	−	2.66321i	−0.469596	−	2.66321i
$785$		0			0
$786$		0			0
$787$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.615661	+	0.788011i	$0.288889\pi$
$787$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.374607	+	0.927184i	$0.377778\pi$
$788$	0.396517	+	0.332717i	0.396517	+	0.332717i
$789$		0			0
$790$		0			0
$791$	1.90381	−	3.29750i	1.90381	−	3.29750i
$792$	−0.0218282	+	0.00794481i	−0.0218282	+	0.00794481i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.916532	−	0.769062i	0.916532	−	0.769062i
$797$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$797$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$798$	−1.79702	−	1.73536i	−1.79702	−	1.73536i
$799$		0			0
$800$	−1.09672	+	0.920260i	−1.09672	+	0.920260i
$801$		0			0
$802$		0			0
$803$	−0.280969	−	1.59345i	−0.280969	−	1.59345i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.503189	−	0.422226i	−0.503189	−	0.422226i
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.848048	−	0.529919i	$-0.822222\pi$
$811$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.309017	+	0.951057i	$0.600000\pi$
$812$		0			0
$813$	0.0736627	−	0.417762i	0.0736627	−	0.417762i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−2.20419			−2.20419
$819$	−0.350958	+	0.294489i	−0.350958	+	0.294489i
$820$		0			0
$821$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$821$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$822$		0			0
$823$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	−0.615661	−	0.788011i	$-0.711111\pi$
$823$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	0.0348995	+	0.999391i	$0.488889\pi$
$824$	−0.00350455	+	0.00607006i	−0.00350455	+	0.00607006i
$825$	0.438371	+	0.759281i	0.438371	+	0.759281i
$826$		0			0
$827$	0.160147	+	0.134379i	0.160147	+	0.134379i	0.719340	−	0.694658i	$-0.244444\pi$
$827$	0.160147	+	0.134379i	0.160147	+	0.134379i	−0.559193	+	0.829038i	$0.688889\pi$
$828$	0.209866	+	0.363498i	0.209866	+	0.363498i
$829$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$829$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$830$		0			0
$831$		0			0
$832$	0.196984	−	1.11715i	0.196984	−	1.11715i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−0.258808	+	1.03802i	−0.258808	+	1.03802i
$837$		0			0
$838$	−2.15602	+	1.80911i	−2.15602	+	1.80911i
$839$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$839$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$840$		0			0
$841$	0.173648	+	0.984808i	0.173648	+	0.984808i
$842$		0			0
$843$	−0.212103	+	0.367373i	−0.212103	+	0.367373i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.990268	+	1.71519i	0.990268	+	1.71519i
$848$	−0.923075	+	1.59881i	−0.923075	+	1.59881i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.104528	−	0.994522i	$-0.466667\pi$
$853$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.997564	+	0.0697565i	$0.0222222\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$857$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$858$	−1.18528	−	0.431408i	−1.18528	−	0.431408i
$859$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	0.913545	+	0.406737i	$0.133333\pi$
$859$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	−0.997564	+	0.0697565i	$0.977778\pi$
$860$		0			0
$861$	1.22249	−	0.444951i	1.22249	−	0.444951i
$862$	0.0502092	−	0.0869649i	0.0502092	−	0.0869649i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	1.18397	+	0.993469i	1.18397	+	0.993469i
$865$		0			0
$866$	−0.804499	−	1.39343i	−0.804499	−	1.39343i
$867$	−0.438371	+	0.759281i	−0.438371	+	0.759281i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.140549	+	0.117935i	−0.140549	+	0.117935i
$873$		0			0
$874$	2.43419	+	0.170215i	2.43419	+	0.170215i
$875$		0			0
$876$	1.16256	−	0.975505i	1.16256	−	0.975505i
$877$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.559193	−	0.829038i	$-0.688889\pi$
$877$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.961262	+	0.275637i	$0.911111\pi$
$878$		0			0
$879$	−0.0528740	−	0.299864i	−0.0528740	−	0.299864i
$880$		0			0
$881$	0.997564	−	1.72783i	0.997564	−	1.72783i	0.438371	−	0.898794i	$-0.355556\pi$
$881$	0.997564	−	1.72783i	0.997564	−	1.72783i	0.559193	−	0.829038i	$-0.311111\pi$
$882$	0.486307	+	0.842309i	0.486307	+	0.842309i
$883$	0.671624	+	0.563559i	0.671624	+	0.563559i	0.913545	−	0.406737i	$-0.133333\pi$
$883$	0.671624	+	0.563559i	0.671624	+	0.563559i	−0.241922	+	0.970296i	$0.577778\pi$
$884$		0			0
$885$		0			0
$886$	1.27028	−	2.20019i	1.27028	−	2.20019i
$887$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$887$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.547850	−	0.459700i	0.547850	−	0.459700i
$892$		0			0
$893$		0			0
$894$	2.46758			2.46758
$895$		0			0
$896$	−0.372866	−	0.135712i	−0.372866	−	0.135712i
$897$	−0.258222	+	1.46445i	−0.258222	+	1.46445i
$898$		0			0
$899$		0			0
$900$	0.123735	−	0.214314i	0.123735	−	0.214314i
$901$		0			0
$902$	−0.825702	−	0.692846i	−0.825702	−	0.692846i
$903$		0			0
$904$	−0.0965283	−	0.167192i	−0.0965283	−	0.167192i
$905$		0			0
$906$	−1.18528	+	0.431408i	−1.18528	+	0.431408i
$907$	0.107320	+	0.608645i	0.107320	+	0.608645i	0.990268	+	0.139173i	$0.0444444\pi$
$907$	0.107320	+	0.608645i	0.107320	+	0.608645i	−0.882948	+	0.469472i	$0.844444\pi$
$908$	0.300580	−	1.70467i	0.300580	−	1.70467i
$909$		0			0
$910$		0			0
$911$	1.69610			1.69610			0.848048	−	0.529919i	$-0.177778\pi$
$911$	1.69610			1.69610			0.848048	+	0.529919i	$0.177778\pi$
$912$	0.779848	−	0.223618i	0.779848	−	0.223618i
$913$	−1.76590			−1.76590
$914$	−1.23256	+	1.03424i	−1.23256	+	1.03424i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	1.26224	+	1.05914i	1.26224	+	1.05914i
$922$	0.230400	+	0.193329i	0.230400	+	0.193329i
$923$		0			0
$924$	−0.928810	+	1.60875i	−0.928810	+	1.60875i
$925$		0			0
$926$		0			0
$927$	−0.00280374	+	0.0159008i	−0.00280374	+	0.0159008i
$928$		0			0
$929$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$929$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$930$		0			0
$931$	2.91540	+	0.203865i	2.91540	+	0.203865i
$932$		0			0
$933$	0.588841	−	0.494096i	0.588841	−	0.494096i
$934$	−2.07126	−	0.753876i	−2.07126	−	0.753876i
$935$		0			0
$936$	0.00403369	+	0.0228762i	0.00403369	+	0.0228762i
$937$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$937$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$938$		0			0
$939$	0.857583	+	1.48538i	0.857583	+	1.48538i
$940$		0			0
$941$	0.160147	+	0.134379i	0.160147	+	0.134379i	0.719340	−	0.694658i	$-0.244444\pi$
$941$	0.160147	+	0.134379i	0.160147	+	0.134379i	−0.559193	+	0.829038i	$0.688889\pi$
$942$	−0.844009	−	1.46187i	−0.844009	−	1.46187i
$943$	−0.635369	+	1.10049i	−0.635369	+	1.10049i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$947$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$948$		0			0
$949$	−1.61803			−1.61803
$950$	−0.630676	−	1.29308i	−0.630676	−	1.29308i
$951$		0			0
$952$		0			0
$953$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$953$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$954$	0.115299	−	0.653891i	0.115299	−	0.653891i
$955$		0			0
$956$	1.12429	−	0.409209i	1.12429	−	0.409209i
$957$		0			0
$958$	0.249824	+	0.432708i	0.249824	+	0.432708i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	0.328048	+	1.86045i	0.328048	+	1.86045i
$965$		0			0
$966$	3.98158	+	1.44918i	3.98158	+	1.44918i
$967$	−1.47274	+	1.23577i	−1.47274	+	1.23577i	−0.559193	+	0.829038i	$0.688889\pi$
$967$	−1.47274	+	1.23577i	−1.47274	+	1.23577i	−0.913545	+	0.406737i	$0.866667\pi$
$968$	0.100418			0.100418
$969$		0			0
$970$		0			0
$971$	−0.160147	+	0.134379i	−0.160147	+	0.134379i	−0.719340	−	0.694658i	$-0.755556\pi$
$971$	−0.160147	+	0.134379i	−0.160147	+	0.134379i	0.559193	+	0.829038i	$0.311111\pi$
$972$	−0.454926	−	0.165580i	−0.454926	−	0.165580i
$973$		0			0
$974$		0			0
$975$	0.823868	−	0.299864i	0.823868	−	0.299864i
$976$		0			0
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.211324	+	0.366024i	−0.211324	+	0.366024i
$982$		0			0
$983$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$983$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$984$	0.0114541	−	0.0649594i	0.0114541	−	0.0649594i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.977310	+	0.435126i	0.977310	+	0.435126i
$989$		0			0
$990$		0			0
$991$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.961262	+	0.275637i	$0.0888889\pi$
$991$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.913545	+	0.406737i	$0.133333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.828150	−	1.43440i	−0.828150	−	1.43440i
$997$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$997$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.c.2001.3	✓	24
11.10	odd	2		2717.1.db.d.2001.2	yes	24
13.12	even	2		2717.1.db.d.2001.2	yes	24
19.16	even	9	inner	2717.1.db.c.2144.3	yes	24
143.142	odd	2	CM	2717.1.db.c.2001.3	✓	24
209.54	odd	18		2717.1.db.d.2144.2	yes	24
247.168	even	18		2717.1.db.d.2144.2	yes	24
2717.2144	odd	18	inner	2717.1.db.c.2144.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.2001.3	✓	24	1.1	even	1	trivial
2717.1.db.c.2001.3	✓	24	143.142	odd	2	CM
2717.1.db.c.2144.3	yes	24	19.16	even	9	inner
2717.1.db.c.2144.3	yes	24	2717.2144	odd	18	inner
2717.1.db.d.2001.2	yes	24	11.10	odd	2
2717.1.db.d.2001.2	yes	24	13.12	even	2
2717.1.db.d.2144.2	yes	24	209.54	odd	18
2717.1.db.d.2144.2	yes	24	247.168	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2717 = 11 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2717.db (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10209 - 0.924765i) q^{2} +(-0.823868 - 0.299864i) q^{3} +(0.185769 - 1.05355i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(0.990268 - 1.71519i) q^{7} +(-0.0502092 - 0.0869649i) q^{8} +(-0.177204 - 0.148692i) q^{9} +O(q^{10})\)	\(q+(1.10209 - 0.924765i) q^{2} +(-0.823868 - 0.299864i) q^{3} +(0.185769 - 1.05355i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(0.990268 - 1.71519i) q^{7} +(-0.0502092 - 0.0869649i) q^{8} +(-0.177204 - 0.148692i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.468969 + 0.812278i) q^{12} +(0.939693 - 0.342020i) q^{13} +(-0.494786 - 2.80607i) q^{14} +(0.869525 + 0.316481i) q^{16} -0.332800 q^{18} +(-0.559193 + 0.829038i) q^{19} +(-1.33017 + 1.11615i) q^{21} +(1.35192 + 0.492057i) q^{22} +(0.294524 - 1.67033i) q^{23} +(0.0152882 + 0.0867035i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(0.719340 - 1.24593i) q^{26} +(0.539776 + 0.934920i) q^{27} +(-1.62308 - 1.36192i) q^{28} +(1.34533 - 0.489660i) q^{32} +(-0.152245 - 0.863423i) q^{33} +(-0.189572 + 0.159070i) q^{36} +(0.150383 + 1.43080i) q^{38} -0.876742 q^{39} +(-0.704030 - 0.256246i) q^{41} +(-0.433799 + 2.46020i) q^{42} +(1.00528 - 0.365893i) q^{44} +(-1.22007 - 2.11322i) q^{46} +(-0.621473 - 0.521478i) q^{48} +(-1.46126 - 2.53098i) q^{49} +(-0.719340 + 1.24593i) q^{50} +(-0.185769 - 1.05355i) q^{52} +(-0.346450 + 1.96482i) q^{53} +(1.45947 + 0.531202i) q^{54} -0.198882 q^{56} +(0.709299 - 0.515336i) q^{57} +(-0.430514 + 0.156694i) q^{63} +(0.567193 - 0.982407i) q^{64} +(-0.966251 - 0.810781i) q^{66} +(-0.743520 + 1.28781i) q^{69} +(-0.00403369 + 0.0228762i) q^{72} +(-1.52045 - 0.553400i) q^{73} +0.876742 q^{75} +(0.769549 + 0.743145i) q^{76} +1.98054 q^{77} +(-0.966251 + 0.810781i) q^{78} +(-0.124187 - 0.704302i) q^{81} +(-1.01287 + 0.368656i) q^{82} +(-0.882948 + 1.52931i) q^{83} +(0.928810 + 1.60875i) q^{84} +(0.0502092 - 0.0869649i) q^{88} +(0.343916 - 1.95045i) q^{91} +(-1.70506 - 0.620589i) q^{92} -1.25521 q^{96} +(-3.95101 - 1.43805i) q^{98} +(0.0401688 - 0.227809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} - 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * q^78 + 6 * q^81 + 3 * q^82 - 12 * q^84 - 3 * q^88 - 6 * q^91 - 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

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